Question 181392
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I presume you meant:


*[tex \Large \text {          }\math f(x) = x^3 + 3x^2 - 5x - 7]


Write the substitution value on the left, draw a vertical line, then write the coefficients of the polynomial.  Leave a space below and then draw a horizontal.  Then drop the first coefficient below the line.


*[tex \LARGE \text {-4   |   1   3   -5   -7}]


*[tex \LARGE \text {--------------------}]
*[tex \LARGE \text {          1              }]


Multiply the substitution value by the number below the line and put it below the second coefficient:


*[tex \LARGE \text {-4   |   1   3   -5   -7}]

*[tex \LARGE \text {            -4          }]


*[tex \LARGE \text {--------------------}]
*[tex \LARGE \text {          1              }]


Add the column just created:


*[tex \LARGE \text {-4   |   1   3   -5   -7}]

*[tex \LARGE \text {            -4          }]


*[tex \LARGE \text {--------------------}]
*[tex \LARGE \text {          1 -1          }]


Repeat the process:


*[tex \LARGE \text {-4   |   1   3   -5   -7}]

*[tex \LARGE \text {            -4     4     }]


*[tex \LARGE \text {--------------------}]
*[tex \LARGE \text {          1 -1   -1     }]


Repeat the process again:



*[tex \LARGE \text {-4   |   1   3   -5   -7}]

*[tex \LARGE \text {            -4     4     4}]


*[tex \LARGE \text {--------------------}]
*[tex \LARGE \text {          1 -1   -1   -3}]


The last addition result is the value of the function when the given value is substituted for the independent variable, hence *[tex \Large f(-4) = -3]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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